Stochastic Thermodynamics and Inference for Nonequilibrium Cooling

Cryogenic electron microscopy has allowed the structure of biomolecules to be studied at near-atomic resolution, relying on the rapid vitrification of a dissolved sample via plunging into a liquid cryogen. Despite its centrality to modern structural biology, both the extent to which this nonequilibrium cooling process affects the conformational ensemble of the dissolved proteins, and whether the original equilibrium ensemble can be recovered from nonequilibrium samples, are unknown. We study these nonequilibrium cooling processes through the lens of stochastic thermodynamics, deriving bounds on entropy production that significantly constrain the space of possible cooling trajectories. These bounds, combined with additional thermodynamic constraints, then allow us to reliably infer the equilibrium ensembles from only samples of rapidly cooled, far from equilibrium ensembles. We validate these methods on both simple models and extensive molecular dynamics simulations of protein vitrification, demonstrating that thermodynamic inference holds promise as a method to recover equilibrium information from nonequilibrium cryo-EM measurements.